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<li class="navelem"><a class="el" href="../../d2/d75/namespacecv.html">cv</a></li><li class="navelem"><a class="el" href="../../d8/d23/classcv_1_1Moments.html">Moments</a></li>  </ul>
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<p>struct returned by <a class="el" href="../../d3/dc0/group__imgproc__shape.html#ga556a180f43cab22649c23ada36a8a139" title="Calculates all of the moments up to the third order of a polygon or rasterized shape. ">cv::moments</a>  
 <a href="../../d8/d23/classcv_1_1Moments.html#details">More...</a></p>

<p><code>#include &lt;opencv2/core/types.hpp&gt;</code></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a0382b98fdb23acdcb05c91a2a44e5a1f"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#a0382b98fdb23acdcb05c91a2a44e5a1f">Moments</a> ()</td></tr>
<tr class="memdesc:a0382b98fdb23acdcb05c91a2a44e5a1f"><td class="mdescLeft">&#160;</td><td class="mdescRight">the default constructor  <a href="#a0382b98fdb23acdcb05c91a2a44e5a1f">More...</a><br /></td></tr>
<tr class="separator:a0382b98fdb23acdcb05c91a2a44e5a1f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab8972f76cccd51af351cbda199fb4a0d"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#ab8972f76cccd51af351cbda199fb4a0d">Moments</a> (double <a class="el" href="../../d8/d23/classcv_1_1Moments.html#a8b1b4917d1123abc3a3c16b007a7319b">m00</a>, double <a class="el" href="../../d8/d23/classcv_1_1Moments.html#a268b19c1ab99f0edcc531f35cfddaee3">m10</a>, double <a class="el" href="../../d8/d23/classcv_1_1Moments.html#a819acd0026a58823b725aea8a0e8b81a">m01</a>, double <a class="el" href="../../d8/d23/classcv_1_1Moments.html#aa5bdd011db458a58c6f73420995528e2">m20</a>, double <a class="el" href="../../d8/d23/classcv_1_1Moments.html#a42016f07a907b360d499ed56239eb245">m11</a>, double <a class="el" href="../../d8/d23/classcv_1_1Moments.html#a708daca15885dba548b635626fdfad5c">m02</a>, double <a class="el" href="../../d8/d23/classcv_1_1Moments.html#af5c394ac23a8587a02fc094107e108af">m30</a>, double <a class="el" href="../../d8/d23/classcv_1_1Moments.html#a9c1f4067e6e201e396ae04f44eb2e6d3">m21</a>, double <a class="el" href="../../d8/d23/classcv_1_1Moments.html#a733a72bcf9d266b24f6216829591b522">m12</a>, double <a class="el" href="../../d8/d23/classcv_1_1Moments.html#ae007b3e092a9b4baf61e83cfecb5aa60">m03</a>)</td></tr>
<tr class="memdesc:ab8972f76cccd51af351cbda199fb4a0d"><td class="mdescLeft">&#160;</td><td class="mdescRight">the full constructor  <a href="#ab8972f76cccd51af351cbda199fb4a0d">More...</a><br /></td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-attribs"></a>
Public Attributes</h2></td></tr>
<tr><td colspan="2"><div class="groupHeader">spatial moments</div></td></tr>
<tr class="memitem:a8b1b4917d1123abc3a3c16b007a7319b"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#a8b1b4917d1123abc3a3c16b007a7319b">m00</a></td></tr>
<tr class="separator:a8b1b4917d1123abc3a3c16b007a7319b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a268b19c1ab99f0edcc531f35cfddaee3"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#a268b19c1ab99f0edcc531f35cfddaee3">m10</a></td></tr>
<tr class="separator:a268b19c1ab99f0edcc531f35cfddaee3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a819acd0026a58823b725aea8a0e8b81a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#a819acd0026a58823b725aea8a0e8b81a">m01</a></td></tr>
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<tr class="memitem:aa5bdd011db458a58c6f73420995528e2"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#aa5bdd011db458a58c6f73420995528e2">m20</a></td></tr>
<tr class="separator:aa5bdd011db458a58c6f73420995528e2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a42016f07a907b360d499ed56239eb245"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#a42016f07a907b360d499ed56239eb245">m11</a></td></tr>
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<tr class="memitem:a708daca15885dba548b635626fdfad5c"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#a708daca15885dba548b635626fdfad5c">m02</a></td></tr>
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<tr class="memitem:af5c394ac23a8587a02fc094107e108af"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#af5c394ac23a8587a02fc094107e108af">m30</a></td></tr>
<tr class="separator:af5c394ac23a8587a02fc094107e108af"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9c1f4067e6e201e396ae04f44eb2e6d3"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#a9c1f4067e6e201e396ae04f44eb2e6d3">m21</a></td></tr>
<tr class="separator:a9c1f4067e6e201e396ae04f44eb2e6d3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a733a72bcf9d266b24f6216829591b522"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#a733a72bcf9d266b24f6216829591b522">m12</a></td></tr>
<tr class="separator:a733a72bcf9d266b24f6216829591b522"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae007b3e092a9b4baf61e83cfecb5aa60"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#ae007b3e092a9b4baf61e83cfecb5aa60">m03</a></td></tr>
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<tr><td colspan="2"><div class="groupHeader">central moments</div></td></tr>
<tr class="memitem:a1f437e60fd477d2ea4b5a3f0c2b8a9d4"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#a1f437e60fd477d2ea4b5a3f0c2b8a9d4">mu20</a></td></tr>
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<tr class="memitem:a811cdd7ac5c644f4678c3d9f1601b44d"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#a811cdd7ac5c644f4678c3d9f1601b44d">mu12</a></td></tr>
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<tr><td colspan="2"><div class="groupHeader">central normalized moments</div></td></tr>
<tr class="memitem:a60e0eda02ec9ed4646673bd2b6b72545"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d23/classcv_1_1Moments.html#a60e0eda02ec9ed4646673bd2b6b72545">nu20</a></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>struct returned by <a class="el" href="../../d3/dc0/group__imgproc__shape.html#ga556a180f43cab22649c23ada36a8a139" title="Calculates all of the moments up to the third order of a polygon or rasterized shape. ">cv::moments</a> </p>
<p>The spatial moments \(\texttt{Moments::m}_{ji}\) are computed as:</p>
<p class="formulaDsp">
\[\texttt{m} _{ji}= \sum _{x,y} \left ( \texttt{array} (x,y) \cdot x^j \cdot y^i \right )\]
</p>
<p>The central moments \(\texttt{Moments::mu}_{ji}\) are computed as:</p>
<p class="formulaDsp">
\[\texttt{mu} _{ji}= \sum _{x,y} \left ( \texttt{array} (x,y) \cdot (x - \bar{x} )^j \cdot (y - \bar{y} )^i \right )\]
</p>
<p>where \((\bar{x}, \bar{y})\) is the mass center:</p>
<p class="formulaDsp">
\[\bar{x} = \frac{\texttt{m}_{10}}{\texttt{m}_{00}} , \; \bar{y} = \frac{\texttt{m}_{01}}{\texttt{m}_{00}}\]
</p>
<p>The normalized central moments \(\texttt{Moments::nu}_{ij}\) are computed as:</p>
<p class="formulaDsp">
\[\texttt{nu} _{ji}= \frac{\texttt{mu}_{ji}}{\texttt{m}_{00}^{(i+j)/2+1}} .\]
</p>
<dl class="section note"><dt>Note</dt><dd>\(\texttt{mu}_{00}=\texttt{m}_{00}\), \(\texttt{nu}_{00}=1\) \(\texttt{nu}_{10}=\texttt{mu}_{10}=\texttt{mu}_{01}=\texttt{mu}_{10}=0\) , hence the values are not stored.</dd></dl>
<p>The moments of a contour are defined in the same way but computed using the Green's formula (see <a href="http://en.wikipedia.org/wiki/Green_theorem">http://en.wikipedia.org/wiki/Green_theorem</a>). So, due to a limited raster resolution, the moments computed for a contour are slightly different from the moments computed for the same rasterized contour.</p>
<dl class="section note"><dt>Note</dt><dd>Since the contour moments are computed using Green formula, you may get seemingly odd results for contours with self-intersections, e.g. a zero area (m00) for butterfly-shaped contours. </dd></dl>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="a0382b98fdb23acdcb05c91a2a44e5a1f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0382b98fdb23acdcb05c91a2a44e5a1f">&#9670;&nbsp;</a></span>Moments() <span class="overload">[1/2]</span></h2>

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          <td class="memname">cv::Moments::Moments </td>
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<p>the default constructor </p>

</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ab8972f76cccd51af351cbda199fb4a0d">&#9670;&nbsp;</a></span>Moments() <span class="overload">[2/2]</span></h2>

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          <td>(</td>
          <td class="paramtype">double&#160;</td>
          <td class="paramname"><em>m00</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double&#160;</td>
          <td class="paramname"><em>m10</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double&#160;</td>
          <td class="paramname"><em>m01</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double&#160;</td>
          <td class="paramname"><em>m20</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double&#160;</td>
          <td class="paramname"><em>m11</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double&#160;</td>
          <td class="paramname"><em>m02</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double&#160;</td>
          <td class="paramname"><em>m30</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double&#160;</td>
          <td class="paramname"><em>m21</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double&#160;</td>
          <td class="paramname"><em>m12</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double&#160;</td>
          <td class="paramname"><em>m03</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
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<p>the full constructor </p>

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<h2 class="groupheader">Member Data Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a8b1b4917d1123abc3a3c16b007a7319b">&#9670;&nbsp;</a></span>m00</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a819acd0026a58823b725aea8a0e8b81a">&#9670;&nbsp;</a></span>m01</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a708daca15885dba548b635626fdfad5c">&#9670;&nbsp;</a></span>m02</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#ae007b3e092a9b4baf61e83cfecb5aa60">&#9670;&nbsp;</a></span>m03</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a268b19c1ab99f0edcc531f35cfddaee3">&#9670;&nbsp;</a></span>m10</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a42016f07a907b360d499ed56239eb245">&#9670;&nbsp;</a></span>m11</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a733a72bcf9d266b24f6216829591b522">&#9670;&nbsp;</a></span>m12</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#aa5bdd011db458a58c6f73420995528e2">&#9670;&nbsp;</a></span>m20</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a9c1f4067e6e201e396ae04f44eb2e6d3">&#9670;&nbsp;</a></span>m21</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#af5c394ac23a8587a02fc094107e108af">&#9670;&nbsp;</a></span>m30</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#adcde8be49f73216d06965df0a884239b">&#9670;&nbsp;</a></span>mu02</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#aa4072d2fd03bc6cdee8a5c0e15fe1b4f">&#9670;&nbsp;</a></span>mu03</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a9afade2efe8ec13e8874acc43f274bf8">&#9670;&nbsp;</a></span>mu11</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a1f437e60fd477d2ea4b5a3f0c2b8a9d4">&#9670;&nbsp;</a></span>mu20</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#aba659bac5ac0ff32cf3ad160d0d3b23e">&#9670;&nbsp;</a></span>mu21</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a1fc9b5378cb0d4c0af043e991b79f96a">&#9670;&nbsp;</a></span>mu30</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#ad15583ebb8f3b85acfb55442a6b8c533">&#9670;&nbsp;</a></span>nu02</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a1b5f0e8a3df615e6bb16f6cd89b9a646">&#9670;&nbsp;</a></span>nu03</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a60e0eda02ec9ed4646673bd2b6b72545">&#9670;&nbsp;</a></span>nu20</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a429e531e475a2619195c4787c4992a62">&#9670;&nbsp;</a></span>nu21</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a223d272dc5ec3efe401d6dd1c4fb3087">&#9670;&nbsp;</a></span>nu30</h2>

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<hr/>The documentation for this class was generated from the following file:<ul>
<li>opencv2/core/<a class="el" href="../../db/dfc/modules_2core_2include_2opencv2_2core_2types_8hpp.html">types.hpp</a></li>
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